Why isn't Bilbo found until the day after the battle?

Answer 1

He was so busy cleaning up after the party and breakfast that he never got around to his normal dusting.
Bilbo had been too busy cleaning up. The dwarves had made their own breakfast and left all the dirty dishes. If he had followed his normal routine, he would have dusted the mantle much earlier in the morning.

Answer 2

Gandalf knew that Bilbo had a habit of cleaning the mantelpiece, an so he left the note there (written on Bilbo's notepaper). However, due to staying up so late the previous night, and the amount of dishes to wash, Bilbo forgot to.

Answer 3

Because he was wearing the ring and was invisible when he got hit with a falling rock and was knocked out.

Answer 4

he is wearing the ring that he took from Gollums cave which makes him invisible when it is on his fingers.

Answer 5

Gandalf told him about it.